Variable conductance standard



March 29, 1960 J. A. CONNOR 2,930,955

VARIABLE CONDUCTANCE STANDARD Filed June 9, 1954 4 Sheets-Sheet 1 H9 Fig, /A Fig. IB

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7 IOS c Til-1 5 ibg/Cs J s C I -L Rs- G5 IT I J Fig. 4

March 29, 1960 Filed June 9, 1954 IOO J. A. CONNOR 2,930,965

VARIABLE CONDUCTANCE STANDARD 4 Sheets-Sheet 2 Fig. 6

[0 K0 lobKc 1.0m: IOMC Gp 5011mm RP, 20,000 ohms Fig, 5

l l I l l Capacitance-(1111f) of C ,Q, or C March 29, 1960 J. A. CONNOR 2,

VARIABLE CONDUCTANCE STANDARD Filed June 9, 1954 Fig. 9

4 Sheets-Sheet 3 S Reciprocal Fomds x IO- l I J s'o so I00 Dial Readings March 29, 1960 J. A. CONNOR 2,930,955

VARIABLE CONDUCTANCE STANDARD Filed June 9, 1954 4 Sheets-Sheet 4 Fig. /2

Dial Reading VOLT United States Patent VARIABLE CONDUCTANCE STANDARD John A. Connor, Haddonfield, N.J., assignor to Leeds and Northrup Company, Philadelphia, lPa., a corporation of Pennsylvania Application June 9, 1954, Serial No. 435,491

2 Claims. (Cl. 323-74) This invention relates to differential loss networks which may be used as variable conductance units of general application and which are particularly suited as precision standards for alternating-current measurements.

Generally in accordance with the invention, a fixed resistance means is effectively transformed to a variable conductance standard by inclusion of the fixed resistance means in a composite network including adjustable reactances whose concurrent values determine the transformation. The equivalent or transformed conductance value is essentially constant throughout a range of frequencies. The reactances are so adjusted that the concurrent incremental changes of their energy-storage factors are of opposite senses and of such magnitudes that the total energy storage of the composite network is essentially constant throughout the range of adjustment of the reactanccs, the effective shunt conductance of the network, however, having different values, each precisely and reproducibly corresponding with concurrent values of the adjustable reactances.

More particularly, a precision standard of adjustable conductance is provided by a two-terminal network in which two adjustable reactances, specifically capacitors, are connected in series between the network terminals and are so mechanically coupled that their combined series-reactance remains essentially constant throughout the range of adjustment. A fixed resistance means is connected in parallel to one of the adjustable reactances. The equivalent shunt conductance of such network varies as a function of the reactance in shunt to the fixed resistance so that, if desired, the operating dial, or equivalent of the adjustable reactance, may be calibrated for direct reading of the equivalent shunt conductance values corresponding with the dial settings. The symmetrical pair of variable loss networks above briefly described may be used with or in measuring circuits of various known types for precise measurement of conductance by direct-substitution methods: they may be used, for example, in quality control measurements of capacitors, coils, cables and other high-frequency components.

For a more detailed understanding of the invention, reference is made to the subsequent description and to the attached drawings in which:

Figs. 1A and 1B show generalized forms of elementary networks;

Figs. 2A and 3A show series and parallel arrangements of an adjustable capacitor and a fixed resistance respectively corresponding with Figs. 1A and 1B;

Figs. 28 and 33 respectively represent the electrical equivalents of Figs. 2A, 3A;

Fig. 4 shows a composite network synthesized from networks of the type shown in Fig. 3A;

Fig. 5A illustrates a preferred form of the network shown in Fig. 4;

Fig. 5B represents the electrical equivalent of Fig. 5A;

ceding and subsequent figures;

Fig. 10, in perspective, shows the internal construction.

and components of the unit of Fig. 9;

Figs. 11 and 12 are graphs referred to in discussion of the unit of Fig. 9;

Fig. 13 schematically illustrates an alternative capacitor arrangement for the unit of Fig. 9;

Fig. 14 schematically illustrates a bridge circuit including composite conductance networks of preceding figures;

Fig. 15 schematically illustrates a Q-meter circuit utilizing composite conductance networks of preceding figures;

Fig. 16 schematically illustrates a bridge circuit including a pair of composite networks of type shown in Fig. 5A.

The networks shown in Figs. 4, 5A, 13 and 14 are composites of rudimentary networks which are first discussed in order that the invention in all of its various illustrated forms may be clearly understood.

Referring to Figs. 1A and 1B, 21 series-combination of resistance (R and reactance (X may be transformed into an equivalent parallel combination of resistance (R and reactance (X or, conversely, a parallel combination of resistance (R and reactance (Xp) may be converted into an equivalent series-combination of resistance (R and reactance (X by means of the following relationships.

For all cases in which Q is large compared to unity, the relationships expressed by Equations 1 and 2 may be more simply expressed as R g-Q and The percent error introduced by use of the simpler approximate expressions (Equations 4- and 5) is. given by the relationship Specifically, for any value of Q greater than 20, the error is less than A When, as shown in Figs. 2A and 3A the reactances are capacitive, the transformation Equations 5 and 4 may be reduced to (10) =GP= wc Rs Itis jtobe noted that the adjustment of capacitor C affects both the energy-loss factor and the energy-storage factor of the network. More specifically, the adjustment of capacitance C changes not only the equivalent shunt conductance G of the network but also the equivalent shunt capacitance C It is further to be noted that the value of capacitance C for a desired value of equivalent shunt conductance depends upon frequency.

Referring to Fig. 3A, the rudimentary network 1UP comprises an adjustable capacitance C in parallel with resistance of fixed value R This network is electrically equivalent to Fig. 3B, the adjustment of capacitance C affording, as -may be derived from Equation 8, adjustment of the equivalent series-resistance R in accordance with .the relation 7 v of adjustable capacitance G for any given value of the equivalent resistance R depends upon frequency. As later explained, these disadvantages of the rudimentary networ'klOP of Fig. 3A are eliminated in the corresponding composite resistance-transformation networks of Figs. 4, 5a and others subsequently described.

Referring to Fig. 4, the network 20F is a series combination of two networks 10P of Fig. 3A in which adjustable capacitors Cp C are oppositely adjusted to maintain constancy of their equivalent total reactance as seen at the networkterminals. Under such conditions, the effective loss variation provided by adjustment of the capacitors is the difference between the conductance variations provided by the two elementary loss networks acting as a differential combination and also as will be shown, such variation of effective loss factor is not a function of frequency. The composite network 20? is therefore free of the two principal disadvantages of the elementary network 3A.

The network 20F of Fig. 4 comprises two seriallyconnected networks, each of which is similar to network 1UP of Fig. 3A in that his a parallel combination of fixed resistance and adjustable capacitance.

The equivalent series-resistance of network 2GP is com prised of two portions respectively related to G and G 1 each in manner above explained in discussion of Figs. 3A, 3B. Thus, the total equivalent series-resistance R of network 20F (as found by applying Equation 9) so i . 4 Expressing the capacitances in terms of elastances, Equation 12 may be rewritten as 5) RT= GnsPa+Gmsm The equivalent total conductance G (Fig. 5B) by analogy to Equation 10 with capacitances expressed in terms of elastances may therefore be written as By substitution of Equation 15 in Equation 16 2 2 (17) G.=GP1( +Gm() As appears from Equation 17, the equivalent shunt conductance of network 20F (Fig. 4) does not depend upon frequency. I

The network P20 of Fig. 5a is the same as network 20P of Fig. 4 except that the resistor in shunt to capacitor C is omitted, i.e., Gpz of Fig. 4 is made of infinite value in network P20 of Fig. 5a. This affords the maximum difference between the loss variation of the two rudimentary networks of network 20F (Fig. 4) as effected by adjustment of capacitors C C For the composite network P20 of Fig. 5a, Equation 17 reduces to 5A and 5B, Equation 18 'is' the basic design equation for conductance standards or units. Since for a particular unit the conductance G may be of fixed value, and since the total elastance of the adjustable capacitors is maintained at fixed values, Equation 18 may be rewrittcnin simpler form as where 7 v in For an adjustment of the capacitors which effects an incremental .increase of elastance of capacitor C51 the corresponding new value of the equivalent shunt conductance G (Fig. 5B) is By subtraction of Equation 19 from Equation 20, it thus appears that The relative change in the equivalen shunt conductance of the standard for such adjustment is therefore AG, ASm

Such relationship is shown by curve A of Fig. 6.

In construction of conductance units or standards of the types shown in Fig. 5A, there are limiting factors to be considered. Again assuming that the permissible error should not be greater than 4%, Q, as defined in Equation 4, should not be less than 20. Such assumption im poses the requirement that for the lowest frequency used, quotient where G is in micromhos C is. in micromi'crofarads. F is in megacycles Additionally assuming that C will ordinarily be no greater than about 250. mrnfi, which is sufficiently large to assure, negligible stray capacitance effects and yet is suiiiciently small for parallel substitution measurements, a. rough maximum-value limitation of 6., may be set at a out. 8.0 micromhos for one m ga yc 8 micromh for 100 kilocycles (see curve B2, Fig. 7) These assumptions also limit the value of R since the maximum value of G is less than but withina few percent of the conductance value G ot resistor R After selection of a value of G within the allowed. range and with knowledge of the maximum afforded by the selected capacitors, the maximum relative change of G can be computed from Equation 18 or ascertained from curve A of Fig. 6,.

A calibration curve. of dial settings vs, equivalent shunt conductance may be made by measurement of C and C and substituting the measured values in Equation 18 for solution of the corresponding values. of G Curves C and C of Fig. 8 are examples of curves so plotted in terms of capacitance; the fixed resistance means used had a conductance of 50 micromhos (20,000v ohms) and the total capacitance C was kept constant at 250 mmfs. From this data can be plotteda G curve in terms of dial setting.

A tw ang dju able onductan un t DG mb dying the composite network P20 of Fig. A is shown in Figs. 9, 10. The terminals 30A, 30B areconnected to the metal housing 31 to provide two ground terminals corresponding with terminal 30 of Fig. 5A. The terminals 32A, 32B are connected to each other to provide two high" terminals corresponding with terminal 32 of Fig. 5A. The two sets of terminals are provided so that as later appears indiscussion of Figs. 14 and 15,, one pair of terminals may be connected to a detector or measuring network with the unknown substituted across the other pair of terminals.

The dial 116 of unit D6 is mechanically connected through an insulated coupling 35 to the rotor shaft of adjustable condenser 34. This shaft is electrically and mechanically connected to the rotor shaft of a second adjustable condenser 36., These two condensers, corresponding with adjustable capacitors C and C of Fig. 5A, are connected in series between the ground and high terminals of the unit. The, plates of; the condensers 34 and 36. are so oriented that as, the capacity of one condenser is increased, the capacity of the other is decreased. However, none of the commonly available adjustable capacitors, i.e., those of the linear capacitance, straight-linefrequency, or straight-line wavelength types continuously affordsthedesired relation defined in Equations 13, 14. For unitD a satisfactory compromise was obtained by padding two straight-line frequency capacitors 34, 36 with adjustable fixed capacitors 39, 4.0. The resulting elastances and condition of tracking are shown in Fig. 11 in which the curve of total elastance S is plotted from the sum of the measured reciprocal capacitances (elastances) S and S of the individual condensers 34, 36 for the various settings of their operating dial 116. The switch 41 (Fig. is operable by knob 42 (Fig. 9) selectively to connect one or the other of fixed resistors 43A, 43B in shunt to condenser 36. Each of resistors; 43A,, .33 rr sponds w th r si tance R91 (couduc auce- 3P1),- o F 5A- These resistors are of low reactance type such as disclosed, for example, in United States, Letters Patent Nos. 1,972,499, 1,972,720 and 2,199,810. The resistance values of these resistors (43A, 438) in the particular unit shown in Figs. 9 and 10 were 100,000 and 50,000 ohms respectively.

Using these two resistors, the calculated incremental conductance ranges. of unit. D are shown by the curves G and G of Fig. 12. The correspondence between the calculated and measured, values is so close, that curves of the. measured values are not drawn.

All conductance measurements made for check of the calculated calibration curves were made by reactance variation techniques described by D. B. Sinclair in the I.R.E Proceedings, volume 26, No. 12, Decemberv 1938. Such techniques though precise are tedious and time-consuming which emphasizes the need for a simple directsubstitution standard oi shunt conductance such as afforded by unit D The need for padding condensers tov obtain constancy of the total elastance of an adjustable conductance standard may be avoided by using an adjustable condenser of thetype schematically illustrated in Fig. 13. In this type, of dual adjustable capacitor, the intermeshing area of the. fixed and movable plates is constant but the spacings between each movable plate 50 and the associated stator plates 51A, 51B are complementarily adjustable.

With suchconstruction, the elastance of capacitance CPL is d (24) S -N where A is plate area d is interplate spacing N is a constant and of condenser Cpg is D d (25) '5': N

where D, is,v a total interplate spacing.

Consequently for all settings the total elastance of the two serially-connected capacitors is which satisfies Equation 14.

Precision loss measurements at radio-frequencies have been made using the adjustable conductance unit D of Fig; 9. The detectors used were of readily available type: specifically a commercial Q-meter was used for parallel (conductance) substitutions: the circuitry and techniques are later more fully discussed in connection with Fig. 15. With suchditferential loss standards, the time required for a measurement is only about two or three minutes as compared to about a half hour required for a measurement using the classical reactance-variation and susceptancevariation methods.

.The differential-loss networks above described have many applications in the field of alternating-current measurements. Some of these applications are shown in Figs. 14 to 16.

For measurement of the etfective conductance of an unknown 6;; by the bridge method, the network P20 of Fig; 5a may be included in one arm of a Wheatstone bridge W2 (Fig. 14). The bridge is balanced twice, once with the network P20 alone in circuit, and once with the unknown G in shunt to network P20. The difference between the two values of efiective conductance of network P20 for which the bridge is in balance is equal to the effective shunt conductance of the unknown G Assuming the adjustable capacitors C and C are constructed and ganged as in discussion of Figs. 9 and 10 or 13, the two effective conductance values of network P20 may be'read from dial 116 (Fig: 9 when calibratedin terms of conductance, or from a chart such as shown in Fig.8. j

For measurements of the effective conductance of an unknown 6;; by the Q-meter or resonance method, the network P20 (Fig. 15) is connected in parallel to the capacitor C (or inductor L) of the series-resonant circuit L, C of the Q-meter. With circuit L, C tuned to resonance at the applied frequency and with a constant injection voltage (e), network P20 is adjusted as above described so that the value of voltage E is the same when the unknown conductance G is connected in shunt to network P20 as when the conductance 6;; is out of circuit. Tthe difference between the two values of the effective conductance G of network 20 for the two adjustments is therefore equal to the conductance 6;; of the unknown. As in the case of the corresponding bridge method (Fig. 14), such two values of the effective conductance G may be read directly from dial 116 (Fig. 9) or from a chart similar to Fig. 8 provided that the capacitors C C are ganged and constructed to provide a constant capacitance as seen at the terminals of the network P20.

In the bridge W4 of Fig. 16, each of two adjacent arms includes a composite network similar to network P20 of Fig. a whose effective shunt conductance is adjustable by a pair of oppositely adjustable capacitors. The four capacitors S S S S of networks 1P, 2P are ganged as indicated by the threaded shaft and nut arrangement 70 for adjustment in unison by dial 11LG.

The adjustable capacitors are so constructed that for all settings of dials 11LG, the relation of their elastances may be expressed as Thus, with bridge W4, the value of an unknown conductance G connected in parallel to one of said arms of the bridge may be determined by adjusting dial llLG for balance. It is to be noted that the unknown conductance is determined by a single balance ratherthan by two as required by bridge W2 of Fig. 14. It is also to be noted that although the change in effective conductance of each of networks 1P, 2P follows a square law (Equation 18), the difference AG between their effective conductances is linear so that equal incremental changes of elastance afford equal incremental changes of the effective shunt conductance transferred from one to the other of the lower bridge arms under discussion.

If the unknown conductance is greater than the effective shunt conductance, preferably to the other arm of the bridge, a selected fixed standard conductance G may be connected in shunt to such other arm and dial 11LG adjusted for a single balance of the bridge. In such case, the value of the unknown conductance is There is no ambiguity in application of Equation 31 as the sign of the incremental elastance change AS of Equation 30 becomes negative when dial 11LG is adjusted in the range for which 52 and S4 are greater than S1 and S3. The dial llLG may be directly calibrated in terms of AG,, the positive and negative value increasing in opposite directions away from the setting for which all of the capacitors are of equal elastance value.

What is claimed is:

1. A two-terminal composite network providing values of effective shunt conductance (G which are each essentially independent of frequency throughout a range of frequencies comprising two rudimentary networks connected in series between thetwo terminals of said composite network, the first of said rudimentary networks essentially consisting of a first parallel combination of fixed resistance R 'and adjustable capacitance C providing a Q of not less than 20 for said range of frequencies, the second of said rudimentary networks essentially consisting of a second parallel combination of fixed resistance R and adjustable capacitance C providing a Q of not less than 20 for said range of frequencies, said adjustable capacitances comprising adjustable condensers coupled for concurrent adjustment in opposite senses and whose plates are shaped to maintain constancy of the total elastance S of the composite network and which provide throughout their range of adjustment a total capacitance C such that the quotient r is greater than for the lowest frequency F of said range when G is in micromhos, C is the micromicrofarads and F is in megacycles, the effective shunt conductance (G of said composite network for concurrent values of said adjustable condensers being where S and S are respectively concurrent values of the elastances of said adjustable capacitances C and C and G and G are the values of the fixed resistances R and R 3 2. A two-terminal composite network as in claim 1 in which one of said fixed resistances is of extremely high value to optimize the range of variation of the equivalent shunt conductance G of the composite network for the range of adjustment of capacitances C and C122. I

References Cited in the file of this patent UNITED STATES PATENTS 2,386,651 Bisson Oct. 9, 1945 2,518,225 Dorst Aug. 8, 1950 2,633,534 Anderson -4--- Mar. 31, 1953 2,695,981 Smoot Nov. 30, 1954 FOREIGN PATENTS 198,522 Switzerland Sept. 16, 1938 UNITED STATES PAT NT OFFICE CERTIFICATE OF 'GORRECTION Patent No, 2 930 965 March 29 1960 John A, Connor It is hereby certified that error appears in the-printed specification of the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 4 line 27 number of the equation for "(1" read (l8) llne 55, equation (20) v for that portion reading "(S 1+SP1) read (S 1+AS 1) Signed and sealed this 4th day of April 19610 (SEAL) Attesti ERNEST W. SWIDER XWWWX ARTHUR w. CROCKER A i Commissioner of Patents Attesting Ofiicer UNITED STATES PATEIIT OFFICE CERTIFICATE OF CORRECTION Patent No. 2 930. 965 March 29 1960 John A0 Connor ears in the-printed specification It is herebfi certified that error app rection and that the said Letters of the above numbered patent requiring cor Patent should read as corrected below.

Column 4 line Z27 number of the equation for "(1" read (18) line 55, equation (20) q for that portion reading "(S 1+SP1) read (S 1-+-AS a Signed and sealed this 4th day of April 19610 (SEAL) Attest! ERNEST W. SWIDER XXXXW XX ARTHUR W. CROCKER A ti Commissioner of Patents Attesting Ofiicer 

